Generalization of low rank parity-check (LRPC) codes over the ring of integers modulo a positive integer

Following the work of Gaborit et al. (in: The international workshop on coding and cryptography (WCC 13), 2013) defining LRPC codes over finite fields, Renner et al. (in: IEEE international symposium on information theory, ISIT 2020, 2020) defined LRPC codes over the ring of integers modulo a prime power, inspired by the paper of Kamche and Mouaha (IEEE Trans Inf Theory 65(12):7718–7735, 2019) which explored rank metric codes over finite principal ideal rings. In this work, we successfully extend the work of Renner et al. by constructing LRPC codes over the ring $$\mathbb {Z}_{m}$$ Z m which is not a chain ring. We give a decoding algorithm and we study the failure probability of the decoder.

Eigenvalue Decomposition Precoded Faster-Than-Nyquist Transmission of Index Modulated Symbols

Postprint accepted on 30 April 2021 for publication in IEEE International Symposium on Information Theory (ISIT), 2021. (c) 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<div>In this paper, we propose a precoded faster-than-Nyquist (FTN) signaling technique for time-domain single-carrier index modulated (IM) symbol transmission. More precisely, eigenvalue decomposition precoding is adopted for the FTN transmission of data bits modulated by single-carrier time-domain IM. While the FTN scheme increases the spectral efficiency and data rate by packing more transmit symbols per block duration than those defined in the Nyquist criterion, time-domain IM works towards the same objective while maintaining symbol sparsity. We analytically derive the constrained capacity of the proposed system. Our simulation results show that the proposed scheme has better bit error ratio (BER) performance over the conventional FTN-IM scheme, particularly for the scenario of a higher packing ratio. In the proposed scheme, $2.5$-dB performance gain is observed at the BER of 10^-4, employing the packing ratio of $0.7$ and the roll-off factor of $0.5$ in a channel-uncoded scenario.<br></div>

Eigenvalue Decomposition Precoded Faster-Than-Nyquist Transmission of Index Modulated Symbols

Postprint accepted on 30 April 2021 for publication in IEEE International Symposium on Information Theory (ISIT), 2021. (c) 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<div>In this paper, we propose a precoded faster-than-Nyquist (FTN) signaling technique for time-domain single-carrier index modulated (IM) symbol transmission. More precisely, eigenvalue decomposition precoding is adopted for the FTN transmission of data bits modulated by single-carrier time-domain IM. While the FTN scheme increases the spectral efficiency and data rate by packing more transmit symbols per block duration than those defined in the Nyquist criterion, time-domain IM works towards the same objective while maintaining symbol sparsity. We analytically derive the constrained capacity of the proposed system. Our simulation results show that the proposed scheme has better bit error ratio (BER) performance over the conventional FTN-IM scheme, particularly for the scenario of a higher packing ratio. In the proposed scheme, $2.5$-dB performance gain is observed at the BER of 10^-4, employing the packing ratio of $0.7$ and the roll-off factor of $0.5$ in a channel-uncoded scenario.<br></div>